Optimized aerodynamic profile for a turbine vane, in particular for a nozzle of the second stage of a turbine

ABSTRACT

When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y, Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point under consideration from a first reference plane P0 situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P1. The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This patent application claims the benefit under 35 U.S.C. §119 to U.S. Provisional Application No. 62/361,558, filed on Jul. 13, 2016, the entirety of which is incorporated herein by reference.

FIELD OF THE DISCLOSURE

The present invention relates to an aerodynamic profile for a turbine vane.

INTRODUCTION

In particular, the invention relates to the aerodynamic profile of a nozzle vane forming a portion of the stator of a gas turbine, and more particularly of a low pressure turbine of the type used in a turbojet of an aircraft.

The invention relates in particular to a nozzle vane of the second stage of a turbine having a plurality of stages, preferably seven stages.

Such a profile should enable the turbine to provide the desired efficiency, and in order to do that it must be such that the flow of air around the profile is sound over the working spectrum of the turbine, i.e. substantially such that it does not give rise to turbulence, which is harmful for overall efficiency.

It must be capable of being installed properly in the environment of the engine, and in particular, for a nozzle vane forming a portion of the stator of the turbine, it must be capable of being fastened easily to the sectors of the foot platform (the zone of the vane that is furthest from the axis of rotation of the turbine) and of the head platform (the zone that is closest to said axis). Furthermore, this part must present a profile enabling it to be manufactured in a reliable and cost-effective manner by available manufacturing methods, such as casting, forging, machining, additive fabrication, or else weaving, without this list being limitative.

Furthermore, the profile of the vane must enable it to withstand the mechanical stresses, to which the vane is subjected, by enabling those stresses to be spread over the entire vane in such a manner as to avoid premature wear thereof. This spreading must apply both in static mode and in dynamic mode.

An object of the invention is to propose an aerodynamic profile for a turbine vane that is optimized, and capable of satisfying those objectives.

This object is achieved by the fact that when cold and in a non-coated state, said profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point P under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane that is the intersection of the stacking axis of the set of vanes and the axisymmetric surface of the hub, out to a second reference plane that is the intersection of said stacking axis with the axisymmetric surface of the casing, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.

This profile has been determined as a result of numerous tests and simulations. It is defined cold, i.e. at an ambient temperature of 20° C. That is a reference temperature at which the profile is geometrically determined. The above-mentioned objectives of aerodynamics and mechanical optimization are naturally valid for the conditions of use of this aerodynamic profile, i.e. when hot, at a temperature that is stabilized when the engine of which the turbine forms a part is being used under cruising conditions.

Furthermore, the aerodynamic profile of the invention is defined in the non-coated state. Since turbine vanes are subjected to high temperature gradients, it is common practice for them to be provided with a coating having thermal properties enabling them more easily to withstand such temperature variations. The profile is determined prior to installing such a coating.

It is stated above that the profile of the invention is “substantially identical” to the nominal profile. This means that the profile may depart very slightly from said nominal profile.

The aerodynamic profile is thus preferably defined within an envelope of ±1 millimeter (mm) in a direction normal to the surface of the nominal profile.

This variation takes account in particular of manufacturing tolerances of the profile.

It is also preferable for the X,Y coordinates of the aerodynamic profile to lie within a range of ±5% relative to the X,Y coordinates of the nominal profile.

This variation takes account of the setting of the profile to adapt to the flow coming from the blades of the turbine situated upstream, so as to further improve the efficiency of the turbine. In particular, the profile is adapted so as to be optimized for the flow coming from the rotary wheel of the first stage of a turbine when the vane of the invention belongs to the nozzle of the second stage of a turbine.

With a nozzle vane, i.e. a portion of the stator of a turbine, the profile serves to orient the fluid correctly for the turbine blades that are situated downstream, and that belong in particular to the rotary wheel of the second stage of the turbine.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be better understood and its advantages appear better on reading the following detailed description of an embodiment given by way of non-limiting example. The description refers to the accompanying drawings, in which:

FIG. 1 is a fragmentary axial section view of a turbine including a vane of profile that corresponds to that of the invention;

FIG. 2 is an enlarged view of FIG. 1, showing the second stage of the turbine.

DETAILED DESCRIPTION

The turbine shown in axial section in FIG. 1 comprises seven stages referenced respectively S1 to S7. In the direction DF going from upstream to downstream, each stage comprises a nozzle that forms a portion of the stator of the turbine and that has a plurality of radially-oriented vanes, and a rotary wheel that forms a portion of the rotor of the turbine and that likewise includes a plurality of radially-oriented blades.

In FIG. 1, the vanes of the nozzles of stages S1 to S7 are given references N1 to N7, whereas the blades of rotary wheels of stages S1 to S7 are given respective references W1 to W7.

In known manner, the vanes of the nozzles are fastened at both ends to stationary structure portions, while the blades of the rotary wheels are fastened to a rotary disk via their roots that are formed at their radially-inner ends closer to the axis of the rotation A of the turbine. The disks d1 to d7 forming parts of the wheels W1 to W7 are constrained to rotate together.

The invention relates in particular to a vane N2 which is a vane of the nozzle of the second stage S2 of the turbine that, as mentioned above, preferably comprises seven stages as shown, without this number being limiting.

As best seen in FIG. 2, via its foot 10, which is its end remote from the axis of rotation A, the vane N2 is fastened to the outer ring 12 of the turbine, which ring is stationary in rotation. Via its head 14, formed by its end closer to the axis of rotation A, the vane is fastened to an inner shroud 16 of the turbine. By convention, the aerodynamic profile 18 of the vane is the entire portion of said vane that extends radially outwards from its head 14 to its foot 10 without incorporating the fastenings respectively to the outer ring 12 and to the inner shroud 16.

In FIG. 2, there can be seen a frame of reference comprising Cartesian coordinates X,Y,Z. The radial direction Z is the height direction of the vane, which extends radially from its head to its foot. This direction Z is perpendicular to the axial direction X which is the direction of the axis of rotation A of the turbine. The direction Y is perpendicular to the X,Z plane and is therefore tangential to the direction of rotation of the turbine.

The nominal profile from which the aerodynamic profile of the invention is determined is defined in following Table 1 of coordinates, in which the coordinate Zadim, measured along the axis Z is non-dimensional, whereas the dimensions X and Y, respectively measured along the axes X and Y, are expressed in millimeters.

TABLE 1 X Y Zadim −16.8932 2.720164 −0.2 −16.9238 2.680798 −0.2 −16.96 2.618035 −0.2 −16.9942 2.511531 −0.2 −16.9995 2.355736 −0.2 −16.9528 2.15776 −0.2 −16.8456 1.927346 −0.2 −16.6777 1.670625 −0.2 −16.4504 1.390787 −0.2 −16.1633 1.091064 −0.2 −15.8163 0.775036 −0.2 −15.4083 0.447855 −0.2 −14.9381 0.116509 −0.2 −14.4042 −0.20944 −0.2 −13.8052 −0.51754 −0.2 −13.1413 −0.79253 −0.2 −12.4143 −1.01553 −0.2 −11.6298 −1.16471 −0.2 −10.7984 −1.21852 −0.2 −9.93847 −1.15789 −0.2 −9.07038 −0.97123 −0.2 −8.21697 −0.65973 −0.2 −7.39716 −0.23323 −0.2 −6.62346 0.291129 −0.2 −5.90181 0.893549 −0.2 −5.23211 1.553494 −0.2 −4.61173 2.253351 −0.2 −4.03881 2.979678 −0.2 −3.51012 3.720261 −0.2 −3.02163 4.464056 −0.2 −2.56969 5.201633 −0.2 −2.15216 5.925488 −0.2 −1.76635 6.628582 −0.2 −1.41014 7.304868 −0.2 −1.08205 7.949231 −0.2 −0.78087 8.557286 −0.2 −0.50566 9.125336 −0.2 −0.25534 9.65019 −0.2 −0.02974 10.1297 −0.2 0.171899 10.56207 −0.2 0.350012 10.94633 −0.2 0.505082 11.28217 −0.2 0.63765 11.57005 −0.2 0.748492 11.81109 −0.2 0.838604 12.00716 −0.2 0.909228 12.1609 −0.2 0.929711 12.28563 −0.2 0.899732 12.36852 −0.2 0.864667 12.41182 −0.2 0.830667 12.43772 −0.2 0.800358 12.45294 −0.2 0.757616 12.46452 −0.2 0.687729 12.46346 −0.2 0.596632 12.41927 −0.2 0.517263 12.31085 −0.2 0.421356 12.16895 −0.2 0.304135 11.99393 −0.2 0.164994 11.78426 −0.2 0.003786 11.53874 −0.2 −0.17943 11.25677 −0.2 −0.38896 10.94128 −0.2 −0.63125 10.59749 −0.2 −0.91183 10.23091 −0.2 −1.23448 9.847449 −0.2 −1.6011 9.45263 −0.2 −2.01165 9.051296 −0.2 −2.46362 8.646297 −0.2 −2.95353 8.239568 −0.2 −3.47666 7.831486 −0.2 −4.02726 7.420943 −0.2 −4.59874 7.005466 −0.2 −5.18554 6.583935 −0.2 −5.78339 6.157132 −0.2 −6.39239 5.731923 −0.2 −7.01735 5.323821 −0.2 −7.66411 4.956626 −0.2 −8.33351 4.65703 −0.2 −9.01467 4.433669 −0.2 −9.69334 4.284668 −0.2 −10.3735 4.194238 −0.2 −11.0346 4.142154 −0.2 −11.63 4.110379 −0.2 −12.2074 4.080141 −0.2 −12.7759 4.031419 −0.2 −13.325 3.956966 −0.2 −13.8444 3.857596 −0.2 −14.3257 3.74067 −0.2 −14.7648 3.616056 −0.2 −15.1607 3.491151 −0.2 −15.5134 3.370849 −0.2 −15.8232 3.258219 −0.2 −16.0905 3.154752 −0.2 −16.3155 3.060462 −0.2 −16.4991 2.975536 −0.2 −16.6433 2.901346 −0.2 −16.7507 2.838837 −0.2 −16.8233 2.787314 −0.2 −17.5428 3.017681 −0.1 −17.5765 2.978806 −0.1 −17.6179 2.916552 −0.1 −17.6614 2.80971 −0.1 −17.68 2.649968 −0.1 −17.6481 2.442602 −0.1 −17.5543 2.197776 −0.1 −17.3981 1.922656 −0.1 −17.1804 1.621092 −0.1 −16.9012 1.296532 −0.1 −16.5603 0.952805 −0.1 −16.1564 0.595186 −0.1 −15.6881 0.230896 −0.1 −15.1534 −0.13037 −0.1 −14.5507 −0.47589 −0.1 −13.879 −0.7894 −0.1 −13.1395 −1.05083 −0.1 −12.337 −1.23674 −0.1 −11.4818 −1.32258 −0.1 −10.5931 −1.28595 −0.1 −9.69347 −1.11492 −0.1 −8.80803 −0.80785 −0.1 −7.958 −0.37639 −0.1 −7.1571 0.16036 −0.1 −6.41163 0.780454 −0.1 −5.7221 1.462494 −0.1 −5.08561 2.18744 −0.1 −4.49899 2.940098 −0.1 −3.95917 3.707945 −0.1 −3.46192 4.47949 −0.1 −3.00242 5.244356 −0.1 −2.57872 5.995004 −0.1 −2.18801 6.724187 −0.1 −1.82768 7.425473 −0.1 −1.49612 8.093596 −0.1 −1.19199 8.724011 −0.1 −0.91418 9.312857 −0.1 −0.66163 9.856907 −0.1 −0.43381 10.3538 −0.1 −0.2297 10.80158 −0.1 −0.04984 11.19971 −0.1 0.106751 11.54768 −0.1 0.240639 11.84593 −0.1 0.352608 12.09563 −0.1 0.44365 12.29874 −0.1 0.515011 12.458 −0.1 0.538305 12.58629 −0.1 0.508356 12.6721 −0.1 0.472084 12.71669 −0.1 0.43674 12.74305 −0.1 0.405005 12.75829 −0.1 0.360353 12.76924 −0.1 0.287962 12.7655 −0.1 0.196191 12.71435 −0.1 0.116123 12.60019 −0.1 0.018144 12.4518 −0.1 −0.10162 12.26885 −0.1 −0.24383 12.04972 −0.1 −0.40868 11.79324 −0.1 −0.59633 11.49889 −0.1 −0.80937 11.16842 −0.1 −1.05211 10.8054 −0.1 −1.32865 10.41399 −0.1 −1.64146 9.998297 −0.1 −1.99201 9.562506 −0.1 −2.38018 9.110255 −0.1 −2.80442 8.644511 −0.1 −3.26215 8.167621 −0.1 −3.74983 7.68127 −0.1 −4.26319 7.186529 −0.1 −4.79776 6.684386 −0.1 −5.3491 6.175943 −0.1 −5.91351 5.663253 −0.1 −6.49112 5.152857 −0.1 −7.0848 4.655251 −0.1 −7.7013 4.187865 −0.1 −8.34782 3.774768 −0.1 −9.02405 3.439523 −0.1 −9.72304 3.204219 −0.1 −10.4318 3.075493 −0.1 −11.1384 3.049433 −0.1 −11.8248 3.107146 −0.1 −12.4734 3.205117 −0.1 −13.0854 3.300334 −0.1 −13.6663 3.372832 −0.1 −14.2165 3.417947 −0.1 −14.7311 3.437559 −0.1 −15.2052 3.43755 −0.1 −15.6362 3.42321 −0.1 −16.0223 3.398011 −0.1 −16.3627 3.364625 −0.1 −16.6572 3.324522 −0.1 −16.9062 3.279954 −0.1 −17.1104 3.233059 −0.1 −17.2715 3.185256 −0.1 −17.3894 3.133497 −0.1 −17.4676 3.084568 −0.1 −18.1879 3.224836 0 −18.2241 3.186225 0 −18.2697 3.1243 0 −18.3211 3.017248 0 −18.3511 2.854434 0 −18.333 2.639108 0 −18.2499 2.382337 0 −18.1031 2.09158 0 −17.8929 1.771626 0 −17.6193 1.426159 0 −17.2821 1.059255 0 −16.8801 0.676207 0 −16.4116 0.284402 0 −15.8741 −0.10585 0 −15.2656 −0.48162 0 −14.5847 −0.82598 0 −13.8319 −1.11776 0 −13.0115 −1.33193 0 −12.1338 −1.44144 0 −11.2182 −1.42217 0 −10.2898 −1.25952 0 −9.37552 −0.95185 0 −8.49859 −0.51169 0 −7.67343 0.039601 0 −6.90687 0.678789 0 −6.19983 1.383543 0 −5.54917 2.133661 0 −4.9505 2.912381 0 −4.40074 3.706866 0 −3.89552 4.505253 0 −3.42976 5.296835 0 −3.00039 6.073274 0 −2.60529 6.827588 0 −2.2417 7.553145 0 −1.90717 8.244166 0 −1.6004 8.896054 0 −1.32016 9.504833 0 −1.06487 10.06698 0 −0.83515 10.58061 0 −0.62988 11.04369 0 −0.44848 11.45516 0 −0.29056 11.81477 0 −0.15551 12.123 0 −0.04255 12.38104 0 0.049315 12.59092 0 0.121327 12.75549 0 0.147216 12.88717 0 0.117249 12.97578 0 0.079811 13.0216 0 0.043175 13.04839 0 0.00904 13.06399 0 −0.03883 13.07422 0 −0.11573 13.06599 0 −0.20822 13.00381 0 −0.29069 12.88017 0 −0.39345 12.72091 0 −0.51908 12.52463 0 −0.66829 12.28959 0 −0.84104 12.01438 0 −1.03787 11.69869 0 −1.26003 11.34336 0 −1.5106 10.95108 0 −1.79103 10.52417 0 −2.1022 10.06527 0 −2.44429 9.577171 0 −2.81694 9.062816 0 −3.21913 8.525192 0 −3.64933 7.967329 0 −4.1056 7.392334 0 −4.58574 6.803438 0 −5.08769 6.204252 0 −5.60965 5.598911 0 −6.15141 4.993243 0 −6.71497 4.395575 0 −7.30527 3.818058 0 −7.92695 3.274702 0 −8.58541 2.784459 0 −9.28486 2.373419 0 −10.0203 2.067597 0 −10.7765 1.885608 0 −11.5294 1.827672 0 −12.2572 1.880518 0 −12.9452 2.017223 0 −13.587 2.203086 0 −14.1842 2.407897 0 −14.7396 2.61213 0 −15.2545 2.804166 0 −15.7295 2.976374 0 −16.1645 3.123832 0 −16.559 3.243878 0 −16.9126 3.333825 0 −17.2242 3.393209 0 −17.4923 3.422782 0 −17.7157 3.420688 0 −17.8923 3.390467 0 −18.0209 3.343535 0 −18.1054 3.293498 0 −18.38 3.260952 0.03 −18.4169 3.222351 0.03 −18.4636 3.160437 0.03 −18.5169 3.053249 0.03 −18.5498 2.889595 0.03 −18.5339 2.672415 0.03 −18.4543 2.41233 0.03 −18.3098 2.117537 0.03 −18.101 1.792869 0.03 −17.8284 1.442084 0.03 −17.4916 1.069335 0.03 −17.0893 0.680075 0.03 −16.6198 0.281759 0.03 −16.0808 −0.11558 0.03 −15.47 −0.49868 0.03 −14.7859 −0.85038 0.03 −14.0288 −1.14914 0.03 −13.2028 −1.36936 0.03 −12.3184 −1.48346 0.03 −11.3953 −1.4668 0.03 −10.459 −1.30448 0.03 −9.53716 −0.99474 0.03 −8.6533 −0.55055 0.03 −7.82201 0.00611 0.03 −7.05019 0.651683 0.03 −6.33882 1.363606 0.03 −5.68436 2.121155 0.03 −5.08295 2.907887 0.03 −4.53074 3.710247 0.03 −4.02331 4.516361 0.03 −3.5563 5.31589 0.03 −3.12589 6.100011 0.03 −2.72954 6.861491 0.03 −2.36457 7.593761 0.03 −2.02912 8.291291 0.03 −1.7216 8.949317 0.03 −1.4407 9.563805 0.03 −1.18527 10.13142 0.03 −0.95502 10.64982 0.03 −0.74928 11.11722 0.03 −0.56746 11.5325 0.03 −0.40916 11.89544 0.03 −0.27378 12.20652 0.03 −0.16054 12.46694 0.03 −0.06844 12.67876 0.03 0.003753 12.84485 0.03 0.030342 12.9775 0.03 0.000357 13.0669 0.03 −0.03741 13.11308 0.03 −0.07441 13.14001 0.03 −0.10934 13.15574 0.03 −0.15826 13.16574 0.03 −0.23665 13.15594 0.03 −0.32919 13.09021 0.03 −0.41264 12.96356 0.03 −0.51702 12.8007 0.03 −0.64463 12.6 0.03 −0.79619 12.35969 0.03 −0.97198 12.0785 0.03 −1.17166 11.75558 0.03 −1.39667 11.39188 0.03 −1.64963 10.98977 0.03 −1.93176 10.55144 0.03 −2.24287 10.0788 0.03 −2.58264 9.574244 0.03 −2.95065 9.040628 0.03 −3.34623 8.48114 0.03 −3.76844 7.899228 0.03 −4.21594 7.298462 0.03 −4.68715 6.682616 0.03 −5.18143 6.056499 0.03 −5.69756 5.424838 0.03 −6.23622 4.794319 0.03 −6.80027 4.174131 0.03 −7.39475 3.576713 0.03 −8.02465 3.017009 0.03 −8.69397 2.513079 0.03 −9.40482 2.088008 0.03 −10.1529 1.767455 0.03 −10.9234 1.570935 0.03 −11.6929 1.501638 0.03 −12.4366 1.549269 0.03 −13.1389 1.688264 0.03 −13.7907 1.887985 0.03 −14.3919 2.119402 0.03 −14.9454 2.360742 0.03 −15.4542 2.596497 0.03 −15.9213 2.814948 0.03 −16.3485 3.007938 0.03 −16.7372 3.169294 0.03 −17.0877 3.294569 0.03 −17.3986 3.384057 0.03 −17.6684 3.439796 0.03 −17.8959 3.452268 0.03 −18.0771 3.427518 0.03 −18.2088 3.38101 0.03 −18.2953 3.330413 0.03 −18.6353 3.290052 0.07 −18.6729 3.251413 0.07 −18.7209 3.18944 0.07 −18.7764 3.081996 0.07 −18.8126 2.917236 0.07 −18.8012 2.697359 0.07 −18.7259 2.432792 0.07 −18.5816 2.133856 0.07 −18.3743 1.803466 0.07 −18.1024 1.446271 0.07 −17.7655 1.066525 0.07 −17.3624 0.669642 0.07 −16.8913 0.263329 0.07 −16.3496 −0.1422 0.07 −15.7351 −0.53344 0.07 −15.0461 −0.89337 0.07 −14.2827 −1.1995 0.07 −13.4492 −1.42596 0.07 −12.5559 −1.54429 0.07 −11.6231 −1.52925 0.07 −10.6769 −1.36557 0.07 −9.74576 −1.05163 0.07 −8.85347 −0.60116 0.07 −8.01476 −0.03671 0.07 −7.237 0.618185 0.07 −6.52058 1.339947 0.07 −5.86182 2.107635 0.07 −5.25717 2.904939 0.07 −4.70225 3.717811 0.07 −4.19256 4.53427 0.07 −3.72347 5.343809 0.07 −3.29157 6.13779 0.07 −2.89403 6.908774 0.07 −2.52815 7.65015 0.07 −2.19162 8.356143 0.07 −1.88305 9.022066 0.07 −1.60136 9.643966 0.07 −1.34521 10.21839 0.07 −1.11429 10.743 0.07 −0.90795 11.21596 0.07 −0.72557 11.63619 0.07 −0.56678 12.00344 0.07 −0.43097 12.3182 0.07 −0.31736 12.5817 0.07 −0.22497 12.79603 0.07 −0.15253 12.96407 0.07 −0.12507 13.09799 0.07 −0.15509 13.18842 0.07 −0.19328 13.23507 0.07 −0.23075 13.26216 0.07 −0.26668 13.27807 0.07 −0.31691 13.28776 0.07 −0.39718 13.27593 0.07 −0.48964 13.20574 0.07 −0.57441 13.07537 0.07 −0.68076 12.90794 0.07 −0.8108 12.70164 0.07 −0.96526 12.45463 0.07 −1.14439 12.1656 0.07 −1.34798 11.83378 0.07 −1.57684 11.4597 0.07 −1.83276 11.04523 0.07 −2.11623 10.59209 0.07 −2.42677 10.10198 0.07 −2.76334 9.576853 0.07 −3.12529 9.019387 0.07 −3.51255 8.433152 0.07 −3.92473 7.821954 0.07 −4.36135 7.189995 0.07 −4.82243 6.542212 0.07 −5.30808 5.88405 0.07 −5.81842 5.221384 0.07 −6.35547 4.562116 0.07 −6.92336 3.916811 0.07 −7.5265 3.297972 0.07 −8.1688 2.720224 0.07 −8.85309 2.201155 0.07 −9.58034 1.762728 0.07 −10.3461 1.430291 0.07 −11.1344 1.22072 0.07 −11.9231 1.140545 0.07 −12.6865 1.181108 0.07 −13.4069 1.32234 0.07 −14.0725 1.535637 0.07 −14.6811 1.79249 0.07 −15.2347 2.069663 0.07 −15.7373 2.349077 0.07 −16.1934 2.616556 0.07 −16.6082 2.859535 0.07 −16.9858 3.068234 0.07 −17.3281 3.236944 0.07 −17.6351 3.362802 0.07 −17.9052 3.444748 0.07 −18.1368 3.474628 0.07 −18.3233 3.45811 0.07 −18.4589 3.412002 0.07 −18.5479 3.360603 0.07 −18.826 3.297434 0.1 −18.8642 3.258724 0.1 −18.913 3.196648 0.1 −18.9699 3.088944 0.1 −19.0082 2.923347 0.1 −18.9982 2.701839 0.1 −18.9236 2.43525 0.1 −18.7826 2.13215 0.1 −18.576 1.797885 0.1 −18.3042 1.436394 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10.99694 1.135014 −5.82373 11.81071 1.135014 −5.52433 12.56072 1.135014 −5.25196 13.24442 1.135014 −5.00678 13.85993 1.135014 −4.78859 14.40615 1.135014 −4.5971 14.88287 1.135014 −4.43217 15.29095 1.135014 −4.29369 15.63238 1.135014 −4.1805 15.90985 1.135014 −4.09182 16.12743 1.135014 −4.05078 16.2983 1.135014 −4.0785 16.41642 1.135014 −4.12198 16.48107 1.135014 −4.16726 16.51945 1.135014 −4.2141 16.54221 1.135014 −4.28026 16.5541 1.135014 −4.38429 16.52225 1.135014 −4.4807 16.40513 1.135014 −4.57738 16.22377 1.135014 −4.69852 15.99114 1.135014 −4.8472 15.705 1.135014 −5.02436 15.36293 1.135014 −5.23032 14.96324 1.135014 −5.46536 14.50525 1.135014 −5.72996 13.98927 1.135014 −6.02368 13.41602 1.135014 −6.34613 12.78707 1.135014 −6.69911 12.10589 1.135014 −7.08529 11.37713 1.135014 −7.50649 10.60575 1.135014 −7.96339 9.796808 1.135014 −8.4563 8.955812 1.135014 −8.98537 8.088751 1.135014 −9.55143 7.202672 1.135014 −10.1573 6.306646 1.135014 −10.8101 5.414618 1.135014 −11.521 4.547928 1.135014 −12.3016 3.732415 1.135014 −13.1611 2.993607 1.135014 −14.0968 2.351642 1.135014 −15.0952 1.818336 1.135014 −16.1345 1.395947 1.135014 −17.1889 1.068112 1.135014 −18.2361 0.806219 1.135014 −19.2584 0.57465 1.135014 −20.2418 0.345074 1.135014 −21.1728 0.097667 1.135014 −22.0455 −0.17871 1.135014 −22.8575 −0.48652 1.135014 −23.6035 −0.8199 1.135014 −24.1194 −1.08354 1.135014 −24.5906 −1.35182 1.135014 −25.0176 −1.62276 1.135014 −25.4009 −1.89561 1.135014 −25.7402 −2.17073 1.135014 −26.0357 −2.44813 1.135014 −26.2872 −2.7278 1.135014 −26.4949 −3.00969 1.135014 −26.6584 −3.29402 1.135014 −26.778 −3.58056 1.135014 −26.8541 −3.86924 1.135014 −28.4128 −5.72476 1.252241 −28.2531 −6.09196 1.252241 −28.0466 −6.42602 1.252241 −27.7969 −6.72845 1.252241 −27.5047 −7.00015 1.252241 −27.1686 −7.24006 1.252241 −26.7889 −7.44842 1.252241 −26.3657 −7.6252 1.252241 −25.8988 −7.77051 1.252241 −25.3883 −7.88412 1.252241 −24.8342 −7.96631 1.252241 −24.2366 −8.01889 1.252241 −23.5953 −8.0432 1.252241 −22.9098 −8.03598 1.252241 −22.1807 −7.99107 1.252241 −21.4103 −7.89844 1.252241 −20.3187 −7.67834 1.252241 −19.2046 −7.32495 1.252241 −18.0964 −6.81573 1.252241 −17.0216 −6.15036 1.252241 −15.9972 −5.34784 1.252241 −15.0314 −4.43106 1.252241 −14.1287 −3.4212 1.252241 −13.2899 −2.33812 1.252241 −12.5113 −1.20141 1.252241 −11.7856 −0.0298 1.252241 −11.1098 1.162881 1.252241 −10.4801 2.36389 1.252241 −9.89121 3.560679 1.252241 −9.33956 4.742685 1.252241 −8.82239 5.900404 1.252241 −8.33728 7.025177 1.252241 −7.88216 8.109098 1.252241 −7.45545 9.145089 1.252241 −7.05693 10.12724 1.252241 −6.6847 11.04963 1.252241 −6.34079 11.90858 1.252241 −6.02423 12.7 1.252241 −5.73574 13.42124 1.252241 −5.47559 14.07037 1.252241 −5.24391 14.64634 1.252241 −5.04096 15.14918 1.252241 −4.86619 15.57962 1.252241 −4.71923 15.93968 1.252241 −4.59936 16.23238 1.252241 −4.50542 16.46173 1.252241 −4.45974 16.6416 1.252241 −4.48485 16.76739 1.252241 −4.52869 16.83689 1.252241 −4.57553 16.87852 1.252241 −4.62594 16.90378 1.252241 −4.69747 16.91618 1.252241 −4.80841 16.87585 1.252241 −4.90611 16.74395 1.252241 −5.00888 16.54668 1.252241 −5.1379 16.29384 1.252241 −5.29613 15.98278 1.252241 −5.48483 15.61101 1.252241 −5.70469 15.17689 1.252241 −5.95609 14.6797 1.252241 −6.23929 14.11964 1.252241 −6.55421 13.49773 1.252241 −6.9006 12.81572 1.252241 −7.28179 12.07808 1.252241 −7.70674 11.29308 1.252241 −8.17786 10.46675 1.252241 −8.6955 9.604742 1.252241 −9.2593 8.713035 1.252241 −9.86947 7.798638 1.252241 −10.5268 6.869766 1.252241 −11.237 5.939577 1.252241 −12.0157 5.034991 1.252241 −12.8779 4.19551 1.252241 −13.8427 3.464957 1.252241 −14.9127 2.875444 1.252241 −16.0657 2.445493 1.252241 −17.2642 2.172945 1.252241 −18.4699 2.014751 1.252241 −19.6597 1.903271 1.252241 −20.817 1.755871 1.252241 −21.9171 1.52535 1.252241 −22.9313 1.195008 1.252241 −23.859 0.7699 1.252241 −24.5541 0.361353 1.252241 −25.1844 −0.08381 1.252241 −25.7494 −0.54622 1.252241 −26.2555 −1.01084 1.252241 −26.708 −1.46866 1.252241 −27.11 −1.91538 1.252241 −27.4636 −2.34923 1.252241 −27.7677 −2.77116 1.252241 −28.0221 −3.18136 1.252241 −28.2269 −3.57986 1.252241 −28.382 −3.96664 1.252241 −28.4876 −4.34168 1.252241 −28.5434 −4.70503 1.252241 −28.5492 −5.05664 1.252241 −28.5039 −5.39615 1.252241

In the above Table 1, the plane Zadim=0 corresponds to the reference plane P0 situated at the base of the profile. This plane P0 is the intersection of the stacking axis AE of the set of vanes with the axisymmetric surface of the hub, i.e. it passes via the intersection between the axis AE and the surface 16A where it is assembled with the inner shroud 16. The plane Zadim=1 corresponds to the reference plane P1 situated at the top of the profile. This plane P1 is the intersection between the axis AE and the axisymmetric surface of the casing, i.e. it passes via the intersection of the axis AE with the surface 12A where it is assembled with the outer ring 12.

By convention, the stacking axis AE of the set of vanes, for the vane of a nozzle, is the axis that extends in the radial direction Z and passes through the middle of the inter-vane throat. For a given vane, the inter-vane throat is the location where the distance between the trailing edge of the vane in question and the suction side of the preceding vane in the direction of rotation of the turbine is at a minimum.

This is the axis on which the various X,Y sections of the set of vanes are “stacked” when designing the set of vanes.

As mentioned at the beginning of the present description, the aerodynamic profile of the invention is substantially identical to the nominal profile defined in the above table, i.e. it departs from said nominal profile by very little at most, being defined in particular within an envelope of ±1 mm in a direction normal to the surface of the nominal profile, and/or having X,Y coordinates lying within a range of ±5% relative to the coordinates X,Y of the nominal profile.

The coordinate Zadim is non-dimensional, i.e. for a point P, situated at a distance D from the plane P0 (where D is measured along the axis Z), the value of Zadim is D/H, where H represents the total height of the profile as measured between the planes P0 and P1. Naturally, in the Table 1 above, by multiplying the coordinate Zadim by the height H, it is possible to obtain the complete coordinates of the vane.

By way of example, the total height H is preferably about 65 mm±10%. By way of example, the plane P0 is situated at a distance of about 360 mm±10% from the axis A.

In the above table, the profile is characterized by twenty-three section planes at constant Zadim coordinates, for which the coordinates X and Y are specified. These twenty-three section planes include nineteen section planes located between Zadim=0 and Zadim=1, and thus arranged in the fluid stream, these section planes being distributed from P0 to P1. The twenty-three section planes also include four section planes which are substantially outside the fluid stream (two section planes with Zadim<0, and two section planes with Zadim>1), these four section planes being provided for ensuring geometric continuity of the stacking, close to the head and the foot, respectively. In each section plane at constant coordinate Zadim, the section of the profile is given by a continuous and smooth curve, interconnecting all of the points (X,Y). In each section plane, the profile is interpolated so as to generate a uniform profile. Between the section planes, the profile is to be interpolated so as to generate a complete vane, as homogeneous as possible.

It is advantageous for the nozzle that includes the vane of the invention to have 140 to 160 vanes that present aerodynamic profiles as defined above. 

We claim:
 1. An aerodynamic profile for a turbine vane, the profile being, when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.
 2. The aerodynamic profile as claimed in claim 1, wherein said profile is defined within an envelope of ±1 mm in a direction normal to the surface of the nominal profile.
 3. The aerodynamic profile as claimed in claim 1, wherein the coordinates X,Y of said profile lie within a range of ±5% relative to the coordinates X,Y of the nominal profile.
 4. The aerodynamic profile as claimed in claim 1, wherein the vane is a nozzle vane forming a part of a stator of a turbine.
 5. The aerodynamic profile as claimed in claim 4, wherein the vane is a nozzle vane of the second stage of the turbine.
 6. The aerodynamic profile as claimed in claim 4, wherein the vane is a vane of the second stage nozzle of a turbine having seven stages.
 7. A turbine vane, presenting an aerodynamic profile as claimed in claim
 1. 8. A turbine, including turbine vanes presenting aerodynamic profiles as claimed in claim
 1. 9. A turbine as claimed in claim 8, including a nozzle that is stationary in rotation, having 140 to 160 vanes that present aerodynamic profiles comprising: when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.
 10. A turbine nozzle forming a portion of a turbine stator, wherein all the vanes of the nozzle present an aerodynamic profile as claimed in claim
 1. 11. A turbine nozzle as claimed in claim 10, including 140 to 160 vanes that present aerodynamic profiles comprising: when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine. 